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We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare…
An algorithm based on quantum phase estimation, which discriminates quantum states nondestructively within a set of arbitrary orthogonal states, is described and experimentally verified by a NMR quantum information processor. The procedure…
We present a hybrid numerical-quantum method for solving the Poisson equation under homogeneous Dirichlet boundary conditions, leveraging the Quantum Fourier Transform (QFT) to enhance computational efficiency and reduce time and space…
Characterization of quantum processes is a preliminary step necessary in the development of quantum technology. The conventional method uses standard quantum process tomography, which requires $d^2$ input states and $d^4$ quantum…
Quantum algorithms for both differential equation solving and for machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in…
Quantum computers have been proposed as a solution for efficiently solving non-linear differential equations (DEs), a fundamental task across diverse technological and scientific domains. However, a crucial milestone in this regard is to…
A recently proposed variational quantum algorithm has expanded the horizon of variational quantum computing to nonlinear physics and fluid dynamics. In this work, we probe the ability of such approaches to capture the ground state of the…
Variational quantum algorithms exploit the features of superposition and entanglement to optimize a cost function efficiently by manipulating the quantum states. They are suitable for noisy intermediate-scale quantum (NISQ) computers that…
Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates…
Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the…
Variational quantum algorithms are one of the most promising methods that can be implemented on noisy intermediate-scale quantum (NISQ) machines to achieve a quantum advantage over classical computers. This article describes the use of a…
Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is…
Quantum scientific computing is to solve engineering and science problems such as simulation and optimization on quantum computers. Solving ordinary and partial differential equations (PDEs) is essential in simulations. However, existing…
Variational quantum algorithms (VQAs) that estimate values of widely used physical quantities such as the rank, quantum entropies, the Bures fidelity and the quantum Fisher information of mixed quantum states are developed. In addition,…
This manuscript explores a variational quantum formulation for nonlinear elasticity problems arising from hyperelastic material models, targeting near term noisy intermediate scale quantum (NISQ) devices. The approach leverages the…
We present a variational quantum algorithm (VQA) to solve the nonlinear one-dimensional Bratu equation. By formulating the boundary value problem within a variational framework and encoding the solution in a parameterized quantum neural…
Preparing the ground state of a system is an important task in physics. We propose a quantum algorithm for preparing the ground state of a physical system that can be simulated on a quantum computer. The system is coupled to an ancillary…
Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. [Suba\c{s}i et al., Phys. Rev. Lett.…
In this study, an algorithm for computing the inverse of periodic k banded matrices, which are needed for solving the differential equations by using the finite differences, the solution of partial differential equations and the solution of…
In this article, we introduce an original hybrid quantum-classical algorithm based on a variational quantum algorithm for solving systems of differential equations. The algorithm relies on a spectral decomposition of the trial functions…